The biggest positive of this year's WPC seems to be that, for the first time in several years, a large number of these rounds look potentially finishable. All are out of 2 points per minute and that means all of the easy puzzles rate as at least 1 minute but more often 2-3 minute puzzles and many others as 5-10 minute puzzles. Contrast this to last year's WPC where a large round like #2 (one hour, 885 points or ~15 points per minute) had 9 of the 36 total puzzles worth less than or equal to 1 minute of time and in only certain cases was this speed possible. Indeed, the top solver of the round was only at about 10.5 points per minute overall. So confidence-wise, unlike last year's super-sized rounds, I won't have the huge struggle with puzzle selection as I will likely spend at least 2 minutes on everything and succeed on a lot of what I spend longer on than that. And aiming for 3-5 potential finishers always seems the best competition goal so I hope this proves to be true.

There are an interesting assortment of rounds, but not very many team rounds -- just two* (weakest links may not end up with the whole team!) -- which is always a fun mode of solving we don't experience anywhere else so I certainly will miss them. Some interesting new styles, but also many that don't excite me as much. There are a LOT of domino puzzles. A whole round of domino dissections (not the most innovative or interesting style to devote a round to, but then most of the ones I've solved are made by computer so we'll see if they've accomplished something more eye opening) and a whole round with one large samurai half domino puzzle which is potentially interesting but also very high variance as even in 9x9 form these are heavy tweaking puzzles sometimes and so the construction of the puzzle will matter a lot here.

So overall it looks like a good two days of puzzling. And then we run into what you could expect is my biggest negative from reading the instructions: the playoffs. I won't expound upon too much more here as I can just link to past posts like this. Quickly, they are set up as match races against other competitors in a 3 round single-elimination structure. On 3 puzzles, you must be faster on exactly 2 to move on (until the final which is out of 5). No time edge, and a slight seed edge but less than in many other tournaments. In short, they are set up less to reward prior performance than to be "entertaining"; I have never viewed this as the goal in a mental sport crowning the world's best, without any television or local media expected from past experience. And they look to undervalue a particular solver(s) strong performance in the qualifying rounds by resetting much of the competition clock not just once but multiple times with races on single puzzles where winning by minutes is just as valuable as winning by a fraction of a second. On 3 puzzles, possibly high variance puzzles, a cautious logical approach can lose two times to luck quite quickly.

I thought an interesting thought experiment would be to look back at WPC 2011's detailed playoff timing with this alternate structure in mind. There, the goal was to finish 9 puzzles first, not to be the fastest on each individual puzzle, so a direct comparison requires certain assumptions such as not treating differently what might be "cautious" Ulrich times, with extra checking, compared to more reckless times like those of later starters. Also that certain information about the puzzles (like how long it took some prior competitors to finish them) does not assist later solvers in choosing modes. But let's say those 9 puzzles were some mix of rounds in this playoff. Cutoffs of the field were done after 3 and 6 so we can even view rounds of 3 like rounds of this competition.

For example, if there had been a 1 vs. 8 quarterfinal in last year's competition, there would have been a storybook match between the Voigt brothers, decided 2-1 for Ulrich. None of the top 4 seeds actually would have fallen (in 2-7, 3-6, or 4-5 matchups), but if any of the seeds 2 (Palmer), 3 (me), 4 (H. Jo), or 9 (Wei-Hwa) -- the eventual top 5 -- had faced Ulrich, Ulrich would have been knocked out over those first three puzzles despite beating all four of those opponents in cumulative time, and by a fair margin (~8.25 minutes to about 10 minutes for Palmer and 11+ minutes for the rest). Winning the hard puzzle by minutes is worth the same as winning the easy puzzle by seconds, and the rest of the competitors had an edge on what might have been a more cautious Ulrich.

Over all 9 puzzles, Palmer would still have beaten Ulrich but in a very tight 5-4 match (PPUPPUUPU). And Palmer only wins a 5 puzzle match in the first few sets of 5 and not the last 5. And I would have beaten either Palmer or Ulrich in 5-4 decisions as well (TTUUTTUTU and TTPPTTPTP) and over all consecutive 5 puzzle matches except for 3-7. This isn't trying to rewrite the podium order, just pointing out the potential for very close results when reduced to single matches even when by total clock time the results aren't this close. Good for excitement, not ranking per se.

And the most interesting result I realized from this analysis is that, over all the puzzles, the champion Palmer was the fastest in the field on exactly 0 puzzles. He was simply very consistent and put up no big numbers. I took 3 golds, 2 silvers, and 2 bronzes, but also took incredible amounts of time on puzzles 3 and 4 which sank my chance of making up ground on the two of them. Ulrich had two firsts (only in the last puzzles) and four other solvers were best on the remaining puzzles. So will my streaky nature work better in this kind of format? Perhaps. On paper, certainly, but on large posterboards and possibly in marker, maybe not. My "reckless" mode needs the ability to erase.

And the analysis is even more interesting in Sudokuland. I'd say my WSC title in 2011 was the most definitive and strongest performance that I've had, with a clear lead on the field before the playoffs and then a visibly dominant performance during the playoffs, but some of that, at least for the audience, came as I started first and no one ever caught up to my desk. Cumulatively I did have the fastest time over 9 puzzles, but I only had the fastest performance on one puzzle, the very last one, which it turns out I'd solved about 6 times before (albeit in a scrambled form) and have used as a milestone puzzle as it was a >10 minute sudoku at the first WPC I attended and now a 3 minute sudoku at the last WSC I attended (7 years apart).

Over the other eight sudoku puzzles in the finals I never posted a big number and was often close to best (like 1 second behind the tied fastest time on puzzle 5), but never golden. Like Palmer, fast and steady won the race, not fastest and less steady. But looking at a single puzzle level, Kota Morinishi was dominant. He won 5 of the 9 puzzles (1, 3, 5, 6, 8) over the field! So I don't need to do the detailed match-ups to know he would win all of them that we have the data for. That includes every first round match-up, and most 5-puzzle match-ups, just from winning so many individual puzzles. He'd get me 6-3 over the set, even though I managed the nine in 29.25 minutes and Kota in 32.5. I'd beat Tiit (5-4) but would lose (4-3) to H. Jo over the seven puzzles we have times for. But H. Jo wouldn't make the playoffs this year as he came from 9th to 4th with his really strong solves.

All of this is wild speculation, and doesn't even account for the advantages that come from being able to choose some of the puzzles you and your opponent will face. I don't really see how this plays as much in sudoku, where having to always choose an easy/medium classic is not a clear "choice" to me yet, and certainly would not work for me if I was competing, but gives classic specialists like Kota or Jakub a potential edge of an easy point in a 3 puzzle match until they have to face each other. But you can imagine, if I'll think this deeply about just the implications of the structure, that I could (and maybe have) gone to some lengths already to analyze solvers' strengths and weaknesses to over-think the simple task of just choosing my best styles all the time. I'm reminded of our "performance heat map" from WSC5, which suggested despite losing his lead that Jan had a huge opportunity to come back over the last 3 puzzles. I wonder what this year's performance heat map will look like, and how multidimensional my game of puzzle-selection chess will be, wherever I end up in the pre-playoff pecking order. I hope to finish 1st in at least one of the two orders, ideally both.